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When there are 'm' rows and 'n' columns in a transportation problem, degeneracy is said to occur when the number of allocations is:
- a)Less than (m + n – 1)
- b)Greater than (m + n – 1)
- c)Equal to (m – n – 1)
- d)Less than (m – n – 1)
Correct answer is option 'A'. Can you explain this answer?
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When there are m rows and n columns in a transportation problem, degen...
Understanding Degeneracy in Transportation Problems
In transportation problems, the concept of degeneracy refers to a situation where not all the available routes (or allocations) are utilized. This can complicate the solution process, particularly in algorithms like the Simplex method.
Criteria for Degeneracy
Degeneracy is said to occur when the number of allocations is less than (m + n - 1), where:
- m = number of supply points (rows)
- n = number of demand points (columns)
Why (m + n - 1)?
- The basic feasible solution for transportation problems typically requires at least (m + n - 1) allocations to maintain a balance between supply and demand.
- If the number of allocations is less than this threshold, it indicates that not all routes are being utilized effectively, leading to redundant or unallocated capacities.
Consequences of Degeneracy
- Multiple Solutions: Degeneracy can result in multiple optimal solutions, making it challenging to find a unique answer.
- Cycle Formation: In certain algorithms, it can lead to cycles, causing the solution process to stall or require special handling.
Conclusion
In summary, the correct answer is option 'A' because degeneracy occurs when the number of allocations falls short of (m + n - 1). Recognizing this condition is crucial for effectively addressing transportation problems and ensuring that solutions are both optimal and feasible.
In transportation problems, the concept of degeneracy refers to a situation where not all the available routes (or allocations) are utilized. This can complicate the solution process, particularly in algorithms like the Simplex method.
Criteria for Degeneracy
Degeneracy is said to occur when the number of allocations is less than (m + n - 1), where:
- m = number of supply points (rows)
- n = number of demand points (columns)
Why (m + n - 1)?
- The basic feasible solution for transportation problems typically requires at least (m + n - 1) allocations to maintain a balance between supply and demand.
- If the number of allocations is less than this threshold, it indicates that not all routes are being utilized effectively, leading to redundant or unallocated capacities.
Consequences of Degeneracy
- Multiple Solutions: Degeneracy can result in multiple optimal solutions, making it challenging to find a unique answer.
- Cycle Formation: In certain algorithms, it can lead to cycles, causing the solution process to stall or require special handling.
Conclusion
In summary, the correct answer is option 'A' because degeneracy occurs when the number of allocations falls short of (m + n - 1). Recognizing this condition is crucial for effectively addressing transportation problems and ensuring that solutions are both optimal and feasible.
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When there are m rows and n columns in a transportation problem, degeneracy is said to occur when the number of allocations is:a)Less than (m + n 1)b)Greater than (m + n 1) c)Equal to (m n 1)d)Less than (m n 1)Correct answer is option 'A'. Can you explain this answer?
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